​This past weekend was easily one of the most exciting weekends of the year for figure skating in the United States: the US National Championships, held this year in St. Paul, Minnesota. There was stunning athleticism and, as all good skating competitions have, a healthy dose of drama. I had an amazing time watching my favorite sport and some of the best moments of the weekend included:​

​Gracie Gold landing seven triple jumps on her way to victory in the ladies long program. In my opinion, when Gracie is ON in competition, she is simply the best. Consistency is problematic for her, so it was nice to see her really own her long program. Intrigued? Watch it in full here.​

The Shib Sibs (short for the Shibutani siblings—yes, really) won the ice dance gold medal. Sometimes I worry that ice dance is “fixed” before the competition even begins. Unlike the other divisions (Men, Ladies, and Pairs), ice dancing rarely has clear-cut falls and mistakes. To move up in the standings you have to make deep improvements to your skating technique and artistry. The Shib Sibs skated a super strong free dance to Coldplay.

And, as always, I couldn’t get enough of the Glitter Twins, i.e. Tara Lipinski and Johnny Weir. Former champions and current skating commentators/TV personalities for NBC, Tara and Johnny make watching skating so much fun. Their outfits, comments, and bedazzled headsets are absolutely crazy and I love it.

​You may be wondering why I would recap this event on a science-focused blog. Yes, I wanted an excuse to write about skating! But, I also wanted to share with you how the sport became increasingly mathematical and technical over the past ten years—something that those outside the skating world may not realize.

In 2004, the ISU Judging System (IJS) replaced the traditional 6.0 scoring system that casual skating fans may remember from the Michelle Kwan era and earlier. The transition to IJS happened in the middle of my competitive skating days and I remember attending tons of seminars to learn about the new system and how to compete within it. The skating community continues to debate and complain about IJS, but overall I enjoy the greater level of insight skaters (and the audience!) get into the outcome of a competition, particularly at the elite level.

Here is what a detailed scoring sheet looks like. This one is actually Gracie’s scores from Saturday night’s long program event. (From US Figure Skating.)

​Don’t worry, this is not IJS 101. But I think it is fascinating how much computation goes into scoring. No longer does a judge give only a technical score and an artistic score. When the international figure skating community developed IJS in the early 2000s, they developed a system that assigns specific values for the difficulty and execution for each element – essentially mapping the artistic sport of figure skating to a mathematical model.

Some differentials in element value are fairly obvious. A double rotation jump is worth more than a single jump. And a triple is worth more than a double. But how much more? And is a triple salchow harder than a triple toe loop? According to IJS, the salchow is more difficult—but I always thought the toe loop was more challenging. So who knows?

And then comes the question of jumps versus spins versus footwork and connecting moves. How is everything weighted relative to each other? What about new moves that skaters develop? These were all questions that had to be answered mathematically and incorporated into the system. It is fascinating to imagine the committee tasked with creating this system. The job of constructing a fair scoring arrangement around an inherently subjective sport that is over a century old is a puzzling and thought-provoking assignment.

Once the IJS was established and the rules set, skaters, coaches, and choreographers had to figure out how to gather the most points—essentially an optimization problem—involving the constraints of the system (the model) and the skater’s skill (probability). They must account for the base value of a maneuver (based on number of rotations in a jump or level in a spin or footwork sequence), the grade of execution (which adds or subtracts from the base value), any bonus for being in the second half of the program (jumps only), and overall deductions, such as falls on a component. This is done for every element, adding up to an astounding number of variables.

So, how do skaters and coaches optimize within this system? Many skaters begin by composing a program that is the most challenging they can realistically achieve. But, is it better to go for a jump you land 95% of the time with lower value or a high-value jump you have a 60% probability of landing? And how many of the risks do you take in a single program?

Perhaps coaches can begin quantifying this with their skaters by keeping metrics on element completion probability--Sabermetrics for figure skating? The overlying question is: what is the expected value for each maneuver a skater performs? Being a nervous nelly at competitions, I always preferred to have a large proportion of my program composed of elements I was confident I could land (85% probability and up) with one or two I was less sure about (60% probability or less). Mentally, I could handle one element that required laser-focus (and possibly a wipe out!), while still maintaining expression and speed through the rest of the program.

Even with access to a larger pool of data, there are intangible elements of skating that come into play: competitive grit, mental toughness, and ability to make changes on the fly in a program. And, for better or worse, these pieces of skating cannot be easily quantified.